If you have to do it yourself anyway, why not make your own projection? I'd do a Dymaxion-style projection onto a truncated icosahedron (Goldberg polyhedron G(1,1), a.k.a. the soccer ball shape), with the poles centered in two of the pentagons, and as many edges as possible over bodies of water. Then I'd print each tile image and plaster it to its own mounting board, trimming the backs of the board edges to 69 degrees on all the hexagons and 73.5 degrees on all the pentagons. At that point, I'd permanently join the tiles with appropriate amounts of contiguous land mass, using brackets, and attach magnets to the remaining edges in such a way that you could assemble them like a puzzle.
I'd rather have a gigantic globe (that can also be dismantled for moving or storage) than have a wall map.
Well, if you want something rectangular, preserving area, with vertical meridians then you automatically end up with a cylindrical area projection. If you want an aspect ratio of 3/2 (approximately) you end up with the Gall-Peters projection. Although if you're prepared to cut out part of the map then you have a lot more freedom in your choice.
Edit: Just discovered that if you prefer a conformal map instead of one with equal area then you end up with the Mercator projection.
"As a retroazimuthal projection, azimuths (directions) are correct from any point to the designated center point." (-- Wikipedia, which knows everything and is never wrong.)
It looks like one retroazimuthal variant (the Craig retroazimuthal) is sometimes called the "Mecca projection", so you know which way to kneel at sundown if you're into that sort of thing.
Which map projections would you choose? A difficult decision: http://en.wikipedia.org/wiki/List_of_map_projections